Multivariable DWN Formulation

This section reviews the DWN paradigm and briefly outlines
considerations arising in acoustic simulation applications. The
multivariable formulation is based on -dimensional vectors of ``pressure''
and ``velocity''
and
, respectively. These variables can be
associated with physical quantities such as acoustic pressure and
velocity, respectively, or they can be anything analogous such as
electrical voltage and current, or mechanical force and velocity. We
call these dual variables Kirchhoff variables to distinguish
them from wave variables [22] which are their
traveling-wave components. In other words, in a 1D waveguide, two
components traveling in opposite directions must be summed to produce
a physical variable. For concreteness, we will focus on generalized
pressure and velocity waves in a lossless, linear, acoustic
tube. In acoustic tubes, velocity waves are in units of volume
velocity (particle velocity times cross-sectional area of the tube)
[27].